Business Finance · Cost of capital and evaluating investment projects

Payback, Discounted Payback and Accounting Rate of Return

Updated 11 October 2026 · Fact-checked

Payback is the time a project takes to recover its initial outlay from cash flows. Discounted payback does the same using discounted cash flows. Accounting rate of return is average accounting profit divided by investment. Add up cash flows until the outlay is recovered, interpolating within the final year. Compare the result with a target.

Understand Payback, Discounted Payback and Accounting Rate of Return

Companies need a way to decide whether a project is worth doing. NPV and IRR use discounted cash flows (DCF) and are the preferred methods. Three simpler methods are also used in practice and examined: payback, discounted payback and accounting rate of return (ARR). You must be able to compute them and explain how they fall short of NPV.

The payback period is the time needed for a project's cumulative net cash inflows to equal the initial outlay. A firm sets a maximum acceptable period, for example 3 years. Projects that pay back sooner are accepted, or ranked higher. It is simple and favours liquidity, but it ignores the time value of money and ignores all cash flows after the payback date.

The discounted payback period discounts each cash flow at the cost of capital first, then finds when the cumulative discounted flows recover the outlay. It fixes the time value problem. It still ignores cash flows after the cut-off. If a project has a positive NPV, its discounted payback must fall within the project life, so discounted payback is consistent with NPV on whether the project ever recovers its cost, but not on ranking.

The accounting rate of return uses accounting profits, not cash flows. It is average annual profit (after depreciation) divided by the investment, either initial or average. Definitions vary, so always state which one you use. ARR ignores timing of profits, depends on accounting policies such as depreciation, and has no link to shareholder value. Its strength is that it uses figures managers already see in the accounts.

The core exam point: NPV measures the value added to shareholders, uses all cash flows and accounts for timing and risk through the discount rate. Payback and ARR do not. Use them as supporting indicators, not as the main decision rule.

Key rules to remember

Payback period: Payback = full years before recovery + (outlay still unrecovered at start of recovery year ÷ cash flow in that year); Assumes cash flows arrive evenly through the year when interpolating. State this assumption.
Discounted cash flow: PV of cash flow in year t = CFt ÷ (1 + i)^t; Use the cost of capital i. Then apply the payback method to cumulative PVs.
Accounting rate of return (initial investment): ARR = average annual accounting profit ÷ initial investment; Profit is after depreciation. Average profit = total profit over life ÷ number of years.
Accounting rate of return (average investment): ARR = average annual accounting profit ÷ [(initial investment + residual value) ÷ 2]; Use this only when the question asks for average investment. Always state the definition used.
Average annual profit: Average profit = (total net cash inflows − total depreciation) ÷ n; Total depreciation = initial cost − residual value, if depreciated straight line.
NPV for comparison: NPV = Σ CFt ÷ (1 + i)^t − initial outlay; Accept if NPV > 0.

How to solve Payback, Discounted Payback and Accounting Rate of Return questions

Use the same routine for any question on these three methods. Keep a small table with years down the side.

1Read the question and note the method asked for, the discount rate (if any), the target period or target ARR, and the ARR definition required.
2List the cash flows by year, with the outlay at time 0 as a negative.
3For payback, build a cumulative cash flow column. Find the year when it turns from negative to non-negative.
4Interpolate: years before recovery + unrecovered amount ÷ cash flow in the recovery year. State the even-flow assumption.
5For discounted payback, first compute each PV = CF ÷ (1 + i)^t, then build the cumulative PV column and repeat the interpolation.
6For ARR, compute total profit after depreciation, divide by the number of years, then divide by the investment base asked for.
7Compare each result with the target and give a decision.
8If asked, comment on weaknesses: time value, flows after cut-off, use of profit, and link to NPV.

Quickest way: Cumulative column and one interpolation

When to use it: Use in MCQs and short written parts where the cash flows are given in a table over a few years.

Write the cumulative column directly from the outlay, adding each inflow in your head.
Spot the last negative cumulative value. The next year is the recovery year.
Compute the fraction as the last negative balance ÷ next year's inflow.
For ARR, use total inflows − outlay (when residual is zero) ÷ years ÷ investment. This avoids listing depreciation.
Check the answer lies between the two year-ends you identified.

Common mistakes in Payback, Discounted Payback and Accounting Rate of Return

Computing payback with undiscounted flows when the question asks for discounted payback.
Students skip the discounting step to save time.
Fix: Always build a PV row first. Cumulative PV should be smaller than cumulative cash flow in every year if i > 0.
Using profit instead of cash flow for payback, or cash flow instead of profit for ARR.
The terms are mixed up under pressure.
Fix: Payback uses cash flows. ARR uses accounting profit after depreciation. Write this beside your working.
Forgetting to deduct depreciation in ARR.
The given annual inflows look like profits.
Fix: Subtract (cost − residual value) ÷ life from each year's inflow, or from the total, before averaging.
Dividing by the wrong investment base in ARR.
Textbooks use both initial and average investment.
Fix: Read the question. If it is silent, use the initial investment and state this clearly.
Interpolating with the wrong denominator, such as total cumulative flow or the first-year flow.
Students lose track of which year recovery happens in.
Fix: Denominator is the cash flow of the recovery year only. Numerator is the balance still unrecovered at its start.
Claiming payback shows profitability or that a short payback means positive NPV.
Short payback sounds like a good project.
Fix: Payback ignores flows after the cut-off, so a project can pay back quickly and still have negative NPV, or pay back slowly and have a high NPV.

Worked examples

Example 1

A project costs ₹10,00,000 now. Net cash inflows are ₹3,00,000 in year 1, ₹4,00,000 in year 2, ₹5,00,000 in year 3 and ₹2,00,000 in year 4. The cost of capital is 10% per year. Find (a) the payback period and (b) the discounted payback period.

Show the solution

Cumulative undiscounted: year 1 = −7,00,000; year 2 = −3,00,000; year 3 = +2,00,000.
Recovery is in year 3. Payback = 2 + 3,00,000 ÷ 5,00,000 = 2.6 years.
PVs at 10%: year 1 = 3,00,000 ÷ 1.1 = 2,72,727; year 2 = 4,00,000 ÷ 1.21 = 3,30,579; year 3 = 5,00,000 ÷ 1.331 = 3,75,657; year 4 = 2,00,000 ÷ 1.4641 = 1,36,603.
Cumulative PV less outlay: year 1 = −7,27,273; year 2 = −3,96,694; year 3 = −21,037; year 4 = +1,15,566.
Recovery is in year 4. Discounted payback = 3 + 21,037 ÷ 1,36,603 = 3.15 years (approximately).

Answer: Payback is 2.6 years. Discounted payback is about 3.15 years. The NPV is +₹1,15,566, so the project is also acceptable on NPV.

Example 2

A machine costs ₹12,00,000 and has a residual value of ₹2,00,000 after 5 years. It is depreciated straight line. Net cash inflows before depreciation are ₹3,00,000 in each of the 5 years. Calculate the ARR (a) on initial investment and (b) on average investment. Then state two weaknesses of ARR compared with NPV.

Show the solution

Annual depreciation = (12,00,000 − 2,00,000) ÷ 5 = ₹2,00,000.
Annual accounting profit = 3,00,000 − 2,00,000 = ₹1,00,000, the same each year, so average profit = ₹1,00,000.
(a) ARR on initial investment = 1,00,000 ÷ 12,00,000 = 8.33%.
Average investment = (12,00,000 + 2,00,000) ÷ 2 = ₹7,00,000.
(b) ARR on average investment = 1,00,000 ÷ 7,00,000 = 14.29%.
Weaknesses: it uses profit, which depends on depreciation policy, instead of cash flow; and it ignores the timing of returns, so a ₹ received later counts the same as one received sooner.

Answer: ARR on initial investment is 8.33%. ARR on average investment is 14.29%. Weaknesses: it depends on accounting policy and ignores the time value of money.

Exam tips

Show the cumulative table. Even if the final answer is wrong, you earn method marks.
State the assumption of even cash flows within the year whenever you interpolate.
State the ARR definition you use. Examiners accept both bases when clearly labelled.
In discussion parts, link each weakness to NPV: time value, all cash flows, and shareholder wealth.
In MCQs, check whether the question says discounted, and whether the flows are cash or profit.

Practice questions from Cost of capital and evaluating investment projects

Payback, Discounted Payback and Accounting Rate of Return in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Payback, Discounted Payback and Accounting Rate of Return: frequently asked questions

What are the advantages and disadvantages of the payback method?

It is simple, easy to explain and highlights liquidity and early risk. It ignores the time value of money, ignores cash flows after the payback date and has an arbitrary cut-off. It does not measure value added to shareholders.

How is discounted payback different from payback?

Discounted payback discounts each cash flow at the cost of capital before accumulating. It therefore allows for the time value of money and is always at least as long as simple payback for a positive discount rate. It still ignores flows after the payback point.

Which formula should I use for accounting rate of return?

Use average annual accounting profit after depreciation divided by the investment base. The base may be initial investment or average investment. If the question does not say, state which you use.

What is the difference between payback and NPV?

Payback gives a time to recover the outlay and ignores later flows and, in its simple form, timing. NPV discounts all flows at the cost of capital and gives the value added in money terms. NPV is the preferred rule for maximising shareholder wealth.